Approximate Hermitian-Yang-Mills structures and semistability for Higgs bundles. II: Higgs sheaves and admissible structures

We study the basic properties of Higgs sheaves over compact K\"ahler manifolds and we establish some results concerning the notion of semistability; in particular, we show that any extension of semistable Higgs sheaves with equal slopes is semistable. Then, we use the flattening theorem to construct a regularization of any torsion-free Higgs sheaf and we show that it is in fact a Higgs bundle. Using this, we prove that any Hermitian metric on a regularization of a torsion-free Higgs sheaf induces an admissible structure on the Higgs sheaf. Finally, using admissible structures we proved some properties of semistable Higgs sheaves.Comment: 18 pages; some typos correcte

Analytic curves in algebraic varieties over number fields

We establish algebraicity criteria for formal germs of curves in algebraic varieties over number fields and apply them to derive a rationality criterion for formal germs of functions, which extends the classical rationality theorems of Borel-Dwork and P\'olya-Bertrandias valid over the projective line to arbitrary algebraic curves over a number field. The formulation and the proof of these criteria involve some basic notions in Arakelov geometry, combined with complex and rigid analytic geometry (notably, potential theory over complex and $p$-adic curves). We also discuss geometric analogues, pertaining to the algebraic geometry of projective surfaces, of these arithmetic criteria.Comment: 55 pages. To appear in "Algebra, Arithmetic, and Geometry: In Honor of Y.i. Manin", Y. Tschinkel & Yu. Manin editors, Birkh\"auser, 200

Bergman kernel and complex singularity exponent

We give a precise estimate of the Bergman kernel for the model domain defined by $\Omega_F=\{(z,w)\in \mathbb{C}^{n+1}:{\rm Im}w-|F(z)|^2>0\},$ where $F=(f_1,...,f_m)$ is a holomorphic map from $\mathbb{C}^n$ to $\mathbb{C}^m$, in terms of the complex singularity exponent of $F$.Comment: to appear in Science in China, a special issue dedicated to Professor Zhong Tongde's 80th birthda

avelumab anti pd l1 in japanese patients with advanced gastric or gastroesophageal junction cancer gc gejc updated results from the phase ib javelin solid tumour jpn trial

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Clinical significance of VEGF-A, -C and -D expression in esophageal malignancies

Vascular endothelial growth factors ( VEGF)- A, - C and - D are members of the proangiogenic VEGF family of glycoproteins. VEGF-A is known to be the most important angiogenic factor under physiological and pathological conditions, while VEGF-C and VEGF-D are implicated in the development and sprouting of lymphatic vessels, so called lymphangiogenesis. Local tumor progression, lymph node metastases and hematogenous tumor spread are important prognostic factors for esophageal carcinoma ( EC), one of the most lethal malignancies throughout the world. We found solid evidence in the literature that VEGF expression contributes to tumor angiogenesis, tumor progression and lymph node metastasis in esophageal squamous cell carcinoma ( SCC), and many authors could show a prognostic value for VEGF-assessment. In adenocarcinoma (AC) of the esophagus angiogenic properties are acquired in early stages, particularly in precancerous lesions like Barrett's dysplasia. However, VEGF expression fails to give prognostic information in AC of the esophagus. VEGF-C and VEGF-D were detected in SCC and dysplastic lesions, but not in normal mucosa of the esophagus. VEGF-C expression might be associated with lymphatic tumor invasion, lymph node metastases and advanced disease in esophageal SCC and AC. Therapeutic interference with VEGF signaling may prove to be a promising way of anti-angiogenic co-treatment in esophageal carcinoma. However, concrete clinical data are still pending

The Quantum McKay Correspondence for polyhedral singularities

Let G be a polyhedral group, namely a finite subgroup of SO(3). Nakamura's G-Hilbert scheme provides a preferred Calabi-Yau resolution Y of the polyhedral singularity C^3/G. The classical McKay correspondence describes the classical geometry of Y in terms of the representation theory of G. In this paper we describe the quantum geometry of Y in terms of R, an ADE root system associated to G. Namely, we give an explicit formula for the Gromov-Witten partition function of Y as a product over the positive roots of R. In terms of counts of BPS states (Gopakumar-Vafa invariants), our result can be stated as a correspondence: each positive root of R corresponds to one half of a genus zero BPS state. As an application, we use the crepant resolution conjecture to provide a full prediction for the orbifold Gromov-Witten invariants of [C^3/G].Comment: Introduction rewritten. Issue regarding non-uniqueness of conifold resolution clarified. Version to appear in Inventione

Development of an experimental platform for the investigation of laser-plasma interaction in conditions relevant to shock ignition regime

The shock ignition (SI) approach to inertial confinement fusion is a promising scheme for achieving energy production by nuclear fusion. SI relies on using a high intensity laser pulse (≈1016 W/cm2, with a duration of several hundred ps) at the end of the fuel compression stage. However, during laser-plasma interaction (LPI), several parametric instabilities, such as stimulated Raman scattering and two plasmon decay, nonlinearly generate hot electrons (HEs). The whole behavior of HE under SI conditions, including their generation, transport, and final absorption, is still unclear and needs further experimental investigation. This paper focuses on the development of an experimental platform for SI-related experiments, which simultaneously makes use of multiple diagnostics to characterize LPI and HE generation, transport, and energy deposition. Such diagnostics include optical spectrometers, streaked optical shadowgraph, an x-ray pinhole camera, a two-dimensional x-ray imager, a Cu Kα line spectrometer, two hot-electron spectrometers, a hard x-ray (bremsstrahlung) detector, and a streaked optical pyrometer. Diagnostics successfully operated simultaneously in single-shot mode, revealing the features of HEs under SI-relevant conditions.T. Tamagawa, Y. Hironaka, K. Kawasaki, D. Tanaka, T. Idesaka, N. Ozaki, R. Kodama, R. Takizawa, S. Fujioka, A. Yogo, D. Batani, Ph. Nicolai, G. Cristoforetti, P. Koester, L. A. Gizzi, and K. Shigemori, "Development of an experimental platform for the investigation of laser–plasma interaction in conditions relevant to shock ignition regime", Review of Scientific Instruments 93, 063505 (2022) https://doi.org/10.1063/5.008996